Monte Carlo dosimetry of the 60Co sources of a new GZP3 HDR afterloading system

Background The purpose of this work was to obtain the dosimetric parameters of the new GZP3 60Co high-dose-rate afterloading system launched by the Nuclear Power Institute of China, which is comprised of two different 60Co sources. Methods The Monte Carlo software Geant4 and EGSnrc were employed to derive accurate calculations of the dosimetric parameters of the new GZP3 60Co brachytherapy source in the range of 0–10 cm, following the formalism proposed by American Association of Physicists in Medicine reports TG43 and TG43U1. Results of the two Monte Carlo codes were compared to verify the accuracy of the data. The source was located in the center of a 30-cm-radius theoretical sphere water phantom. Results For channels 1 and 2 of the new GZP3 60Co afterloading system, the results of the dose-rate constant (Λ) were 1.115 cGy h−1 U−1 and 1.112 cGy h−1 U−1, and for channel 3 they were 1.116 cGy h−1 U−1 and 1.113 cGy h−1 U−1 according to the Geant4 and EGSnrc, respectively. The radial dose function in the range of 0.25–10.0 cm in a longitudinal direction was calculated, and the fitting formulas for the function were obtained. The polynomial function for the radial dose function and the anisotropy function (1D and 2D) with a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\uptheta$$\end{document}θ of 0°–175° and an r of 0.5–10.0 cm were obtained. The curves of the radial function and the anisotropy function fitted well compared with the two Monte Carlo software. Conclusion These dosimetric data sets can be used as input data for TPS calculations and quality control for the new GZP3 60Co afterloading system.


Background
The use of high-dose-rate (HDR) brachytherapy is a highly widespread practice around the world. The International Commission on Radiation Units and Measurement (ICRU) report 89 recommends 60 Co and 192 Ir as HDR sources [1]. Because the geometry of the 192 Ir source is smaller and its energy is lower compared to that of the 60 Co source, the 192 Ir source is the primary HDR source in clinical practice. The 60 Co source results in increased toxic reactions and the issue of radiation protection. Although not as widespread as the 192 Ir source, the 60 Co source is also available on remote afterloading systems dedicated to HDR brachytherapy, mainly for the treatment of gynecological cancer [2,3]. The 60 Co source has the advantage of a longer half life compared with the 192 Ir source [4], which provides a longer duration of clinical use and reduced operating costs. Thus, the 60 Co brachytherapy source is certainly more cost-effective for developing countries [5,6]. The GZP3 and GZP6 60 Co HDR afterloading systems, manufactured by the Nuclear Power Institute of China (NPIC), are widely used at home and abroad. Several studies have been performed on the GZP 60 Co source [7][8][9], including the GZP3 and GZP6 models. The dosimetric data for GZP6 60Co source number 3 were obtained by Lei et al. [7] using Monte Carlo (MC)-based dosimetry. Wang et al. [9] calculated the dosimetric data for the GZP3 60Co source using the MC simulation, EGSnrc.
Recently, a new GZP3 60 Co HDR afterloading system was manufactured by NPIC, and it has been introduced in brachytherapy procedures. It has three channels in the HDR system; the sources of channels 1 and 2 have the same design while the source of channel 3 has a different design.
According to the recommendations of the American Association of Physicists in Medicine (AAPM) and the European Society for Radiotherapy and Oncology (ESTRO) [10], the dosimetric parameters of all brachytherapy sources must be based on the Radiation Therapy Committee Task Group No. 43 (TG43 and TG43U1) formalism before their clinical use and must be obtained by either experimental or MC methods [11,12]. Because of the different source designs, the dose distribution for each source model is different; therefore, dosimetric data from different sources cannot be used with each other. MC simulation is widely used in brachytherapy; however, for the new GZP3 60 Co HDR sources, there are no dosimetric data available in the literature, based on a comprehensive determination of TG43 and TG43U1.
This study aimed at obtaining the full dosimetric data (i.e., the dose-rate constant, radial dose function and anisotropy function) of the new GZP3 60 Co source channels 1, 2 and 3, following the TG43 and TG43U1, using the Monte Carlo codes Geant4 and EGSnrc. The dosimetric data derived in this work were compared with the available data for similar 60 Co sources. These dosimetric data can be used in treatment planning systems (TPS) as input data and to validate TPS calculations.

Radioactive source structure
The geometric design and materials of the new GZP3 60 Co afterloading system were provided by the manufacturer and are shown schematically in Fig. 1. The new GZP3 HDR afterloading system is comprised of two different 60 Co Fig. 1 A schematic view of the new GZP3 60 Co afterloading system channel 1, 2 and 3. Dimensions are given in mm sources affixed to three channels in the system. It is composed of a central cylindrical active core made of 60 Co with a density of 8.9 g/cm 3 , 0.5 mm in radius, 1 mm in length for channels 1 and 2, and 2 mm in length for channel 3. The radioactive 60 Co is distributed uniformly throughout the core. The active core is encapsulated in a 2.1-mm-diameter and 5.8-mm-long cylinder made of stainless steel for channels 1 and 2. The mass density and composition of the materials are shown in Table 1.

Dose-calculation formalism
The 1D and 2D dose calculation formalism proposed by the AAPM TG43 report was followed [11]. According to this formalism, the 1D equation used to calculated dose rate, as shown in Eqs. (1). The 2D dose rate, Ḋ (r, θ), at point (r, θ) in the medium, where r is the distance in cm form the active source center and θ is the polar angle relative to the longitudinal axis of the source, as shown in Eqs. (2): where S k is the source-air-kerma strength in units of U (1U = 1 μGy m 2 h −1 = 1 cGy cm 2 h −1 ). The reference distance r 0 and angle θ 0 are 1 cm and π/2, respectively.
Λ is the dose-rate constant defined as the ratio of dose rate to water at the reference point (r 0 , θ 0 ) and air-kerma strength, G(r,θ) is the geometry factor, defined as where L is the active length of the source, and β is the angle subtended by the active source with respect to the point (r,θ).
The value g(r) is the radial dose function, defined as The value φ an (r) is the 1D anisotropy function, defined as and F(r,θ) is the 2D dose-anisotropy function, defined as

Monte Carlo calculations
In this study, we employed the Monte Carlo codes Geant4 (version 10.4) [13] and EGSnrc [14] to derive all dosimetric parameters of the new GZP3 60 Co sources, following the formalism described by TG43 and TG43U1. These MC codes have been successfully and widely used in dosimetric studies of brachytherapy [15][16][17][18]. Different MC codes used different physics models and different cross-sections of data in the transport of electrons. The low-energy physics model of Geant4 was used. This physics model uses the EPDL97 cross sections [19] for photons and EEDL [20] for electrons. For the EGSnrc, the photon cross sections from the XCOM database [21] were used. The cutoff energy was set to 10 keV for both photons and electrons. The 60 Co spectrum was obtained from the NuDat database, taking only the two gamma photons with 1.17 and 1.33 MeV of energy in the simulation [22]. The contribution of the β spectrum to the dose was not considered in the simulation due to the absorption with stainless steel cover around the metallic 60 Co, with the total dose of electrons less than 1% at distances greater than 1.0 mm from the source [23,24].
In order to obtain the dose distribution in water, the 60 Co source was located at the center of a spherical liquid water phantom with a 30-cm radius in the simulation, which acted as an unbounded phantom [25]. Three different grid sizes were used to score the absorbed dose at distances from the center of the source r ranging from 0.25 to 10.0 cm and polar angles ranging from 5° to 180°. The first was composed of cylindrical rings 0.025 cm thick and 0.005 cm high, for 0 cm < r ≤ 1.0 cm; the second was composed of cylindrical rings 0.05 cm thick and 0.05 cm high, for 1 cm < r < 3.0 cm; and the third one was composed of cylindrical rings 0.1 cm thick and 0.1 cm high, for 3.0 cm ≤ r ≤ 10.0 cm. In the coordinate system, θ, y, and z are representative of the polar angle and radial and axial coordinates, respectively. The coordinate axes used are shown in Fig. 1. The dose absorbed in the water was calculated in Geant4 using the function of GetTo-talEnergyDeposit, whereas in EGSnrc the tally afforded within the DOSRZnrc package was used. The absorbed dose were calculated to obtained radial dose function and anisotropy function in spherical (r, θ) and cylindrical (y, z) coordinates. In spherical coordinates, r is defined as the distance from the center of the source. In cylindrical coordinates, y and z are representative of the radial and axial coordinates, respectively. When z = 0, we set up the cylindrical rings at y ranging from 0.25 cm to 10 cm to obtain the absorbed dose D(y, z), and then used equation g(r) to calculated the radial dose function. Simultaneously, we set up cells at the same distances as those used in the cylindrical coordinate system (0.25 cm ≤ r ≤ 10.0 c), and θ ranged from 5˚ to 180˚ while obtaining the absorbed dose D(r, θ), and then we calculated the anisotropy function by equation F(r, θ). Due to the high energy of the 60 Co, electronic equilibrium was reached at a distance of about 1.0 cm. The differences between dose and kerma were 1.5% at 0.5 cm from the source, less than 0.5% at 0.7 cm and negligible at distances greater than 1.0 cm [23]. Thus, the dose cannot be approximated by kerma at very small distances (< 0.5 cm), unlike 192 Ir and 137 Cs sources. In order to accelerate calculations and reduce statistical uncertainty and the computation time, kerma was obtained for r > 0.7 cm. To estimate the air-kerma strength, the 60 Co source was located in the center of a 3 × 3 × 3-m-cubed air phantom. As TG43U1 recommended [12], the air used in this simulation had 0% humidity. The cylindrical ring was used to score for kerma of 0.1 cm in height and 0.1 cm in diameter.
The number of photon histories was 5 × 10 9 to obtain dose values and 2 × 10 9 photon histories to obtain kerma values.

Dose-rate constant
The air-kerma strength, S k , was calculated by using Geant4 and EGSnrc. Its values were 2.985 × 10 -7 and 2.981 × 10 -7 cGy cm 2 h −1 Bq −1 for channels 1 and 2, and 2.975 × 10 -7 and 2.969 × 10 -7 cGy cm 2 h −1 Bq −1 for channel 3. The dose-rate constant for the 60 Co source were found to be equal to 1.115 ± 0.004 and 1.112 ± 0.004 cGy h −1 U −1 for channels 1 and 2 and 1.116 ± 0.004 and 1.113 ± 0.004 cGy h −1 U −1 for channel 3. These results are presented in Table 2, along with the corresponding values calculated for the similar 60 Co HDR sources. The difference between the dose-rate constants of channels 1, 2 and 3 with two Monte Carlo codes were 0.27% and 0.27%, respectively. Furthermore, Table 2 shows that all the dose-rate-constant values with different sources matched closely (within 2.87%) and the values of the new GZP3 60 Co sources were slightly higher than the other types (GZP6, BEBIG and Flexisource) of 60 Co sources.

Radial dose functions and anisotropy functions
The values of the radial dose function g(r) of the new GZP3 60 Co source for radial distances from 0.25 to 10.0 cm by two MC codes are presented in Table 3. Table 3 and Fig. 2 show that the g(r) values between the two MC codes match well; the differences were less than 0.55% for channels 1 and 2 and less than 0.58% for channel 3. The differences in Fig. 2 were calculated as follow: (g EGSnrc -g Geant4 )/g Geant4 , where g EGSnrc and g Geant4 represent the values of the radial dose function for the EGSnrc and Geant4, respectively. The radial dose function obtained for the new GZP3 60 Co source is compared with similar sources from the relevant literature in Fig. 3. The differences in Fig. 3 were calculated as follow: (g GZP3 -g others )/g GZP3 , where g GZP3 and g others represent the values of the radial dose function for this work by Geant4 and others work, respectively. This comparison shows that the curves of the g(r) were very similar at r > 1 cm and small differences were present at r < 1 cm. The results of our calculations of channels 1 and 2 were compared with those of Ballester et al. [24] for the BEBIG 60 Co source by Geant4: for 0.25 ≤ r ≤ 1.0 cm, the differences were less than 4.64% and for 1 < r ≤ 10.0 cm, they were less than 0.32%. These differences were due to varying degrees of photon scattering and absorption in the sources, while the differences in the dimensions and encapsulation designs of the sources were negligible [27,28]. The radial dose functions obtained by Geant4 were fitted to a fifth-order polynomial function over the range of 0.25 ≤ r ≤ 10.0 cm according to: The values of the fitted parameters were as follows: (a) for channel 1 and 2, R 2 = 0.995, a0 = − 0.023, a1 = 0.112, g(r) = a0r −2 + a1r −1 + a2 + a3r + a4r 2 e −a5r a2 = 0.885, a3 = − 0.112, a4 = 0.004 and a5 = 0.149; and (b) for channel 3, R 2 = 0.995, a0 = − 0.022, a1 = 0.102, a2 = 0.895, a3 = − 0.11, a4 = 0.004 and a5 = 0.142. The overall accuracy of the fits was excellent; the maximum deviations were less than 0.46% and 0.41% for channels 1, 2 and 3, respectively.
In Tables 4 and 5, the full data for the 1D and 2D anisotropy functions by Geant4 and F(r, θ) are presented at radial distances r = 0-10.0 cm and at polar angles θ = 0°-175°. The F(r, θ) values for the selected radial distances of 1.5 cm, 3.0 cm, 5.0 cm and 7.0 cm are presented in Fig. 4. In this figure, it can be seen that, at the polar angles close to the long axis, the values of the F(r, θ) presented a non-smooth shape with F(r, θ) values significantly lower than the other angles (30° ≤ θ ≤ 150°), which was due to the oblique filtration within the source design.

Dose-rate distribution and uncertainties
The along-away 2D-dose-rate results (cGy h −1 U −1 ) for the channel 1, and 2 and 3 60 Co source for quality assurance (QA) purposes are presented in Tables 6 and  7, respectively. The QA values were tabulated over the ranges of − 10 cm ≤ z ≤ 10 cm and 0 ≤ y ≤ 10 cm.
The uncertainties in the final dose-rate distributions for the 60 Co sources, including statistical uncertainty (type A) and systematic uncertainty (type B), were calculated as recommended by TG43U1. 9 The statistical uncertainty of the 60 Co source depended on the axial position z and the longitudinal position y. In this study, the statistical uncertainty was less than 0.72% and 0.73% for the points located on or very near to the longitudinal axis and less than 1.21% and 1.19% for the other points, for channels 1, 2, and 3 by Geant4, respectively.  For the new 60 Co source, the main source of a systematic uncertainty based on the Geant4 simulation was the source geometry. The tolerances of this new source to the active core diameter were ± 0.05 mm, as provided by the manufacturer. For + 0.05 mm on the new source diameter, the uncertainty was less than 1.34% for channels 1 and 2, and was 1.42% for channel 3 in the ranges of − 10 cm ≤ z ≤ 10 cm and 0 ≤ y ≤ 10 cm, respectively. For − 0.05 mm on the new source diameter, the uncertainty was less than 1.24% for channels 1 and 2, and was 1.35% for channel 3, respectively. For the 60 Co spectrum, the dominant interaction is the Compton effect. All the tabulated cross sections data are well established. Thus, as suggested in previous works [24,29], the uncertainty in cross sections and energy spectrum were negligible. Thus, the quadrature sum of these three terms gives a total uncertainty of 2.19% for channels 1 and 2, and 2.29% for channel 3, respectively (type A and type B).

Conclusion
In this study, the full dosimetric parameters for the new GZP3 60 Co sources were obtained using the Monte Carlo Geant4 and EGSnrc codes, based on the dose-calculation formalism recommended by the AAPM TG43 and TG43U1 reports. The dose-rate constant, radial dose function, anisotropy function and away-along dose-rate